In this exercise the goal is to extend the Math() object adding four methods for calculate different types of averages.

• Arithmetic Mean: The division of the sum of the numbers by the quantity of numbers.
  • avg of [A, B, C] ➞ (A + B + C) / 3
• Quadratic Mean: Also called Root Mean Square, is the square root of the arithmetic mean of the squared numbers.
  • qAvg of [A, B, C] ➞ ²√ ( (A² + B² + C²) / 3 )
• Harmonic Mean: is the reciprocal of the arithmetic mean of the numbers reciprocals.
  • hAvg of [A, B, C] ➞ ( (A⁻¹ + B⁻¹ + C⁻¹) / 3 )⁻¹
• Geometric Mean: is the n-th root of the product of the numbers, where n is the quantity of numbers.
  • gAvg of [A, B, C] ➞ ³√ (A * B * C)

For each average type build a function that, given a required parameter (the array containing the numbers) and an optional one (the precision, or number of floating digits to return) returns the result as a number.

Examples

Math.avg([3, 5, 7])➞ 5
//Precision is an optional parameter.
// (3 + 5 + 7) / 3 = 15 / 3 = 5

Math.qAvg([3, 5, 7], 1) ➞ 5.3
// ²√ ( (3² + 5² + 7²) / 3 ) = ²√ (83 / 3) = 5.3

Math.hAvg([3, 5, 7], 1) ➞ 4.4
// Precision is required only for the final result.
// (3⁻¹ + 5⁻¹ + 7⁻¹) / 3 )⁻¹ = (0.676... / 3)⁻¹ = 4.4

Math.gAvg([3, 5, 7], 1) ➞ 4.7
// ³√ (3 * 5 * 7) = ³√ 105 = 4.7

Notes

• Pay attention to cumulative rounding errors! Precision is required only if the parameter is indicated and only for the final result.
• All given arrays are valid ones containing positive numbers greater than zero, either integers or float.
• REVISION NOTE: Implementing a method for to get the n-th root of a number can lead to rounding imprecisions if you use a combination of exponential and logarithm instead of a direct formula. Thanks to @Pustur and @xAlien95, see the Comments tab for more info. After the update, some old solution could fail the last test for the geometric average.